1. LECTURE UNIT NO. 1
I. Carnot Cycle (TSTS)
- most efficient cycle
- Basis of comparison for Rankine Cycle
Flow Diagram:
PV diagram:
1
2
4
3
TS diagram:
1 2
4 3
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2. DEFINITIONS: During a certain process
Expansion Ratio: re = Vmax / Vmin
Compression Ratio: rk = Vmax / Vmin
Cut off Ratio: rc = Vmax / Vmin
Pressure Ratio: rp = Pmax / Pmin
EQUATIONS:
1. PVT Relationships:
Process: 1 – 2 Isothermal Heat Addition Process (T = C)
P2V2 / T2 = P1V1 / T1
V2 / V1 = P1 / P2 = re (T=C)
Process: 2 - 3 Isentropic Expansion Process (S = C)
T3 / T2 = (P3 / P2) k-1 / k = (V2 / V3) k-1
(T3 / T2) 1/ k-1 = (P3 / P2) 1 / k = V2 / V3
(T2 / T3) 1/ k-1 = (P2 / P3) 1 / k = V3 / V2 = re (S=C)
Process: 3 - 4 Isothermal Heat Rejection Process (T = C)
P4V4 / T4 = P3V3 / T3
V3 / V4 = P4 / P1 = rk (T=C)
Process: 4 – 1 Isentropic Compression Process (S = C)
T1 / T4 = (P1 / P4) k-1 / k = (V4 / V1) k-1
(T1 / T4) 1/ k-1 = (P1 / P4) 1 / k = V4 / V1 = rk (S=C)
NOTE:
A. Isentropic expansion ratio = Isentropic compression ratio
re (S=C) = rk (S=C)
V3 / V2 = V4 / V1
B. Isothermal expansion ratio = Isothermal compression ratio
re (T=C) = rk (T=C)
V2 / V1 = V3 / V4
Hence:
P1 / P2 = V2 / V1 = V3 / V4 = P4 / P3
2. Heat Added, QA = Σ + Q
Process: 1 - 2 (T=C)
Q1-2 = P1V1 ln V2 / V1 = P2V2 ln V2 / V1
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3. 3. Heat Rejected, QR = Σ - Q
Process: 3 – 4 (T=C)
Q3-4 = P3V3 ln V4 / V3 = P4V4 ln V4 / V3
4. Network, Wnet
Wnet = | QA | - | QR |
= | mRT1 ln P1 / P2 | - | - mRT4 ln P1 / P2 |
Wnet = mR(T1 – T4) ln P1 / P2
5. Carnot Cycle Thermal Efficiency, ecc
ecc = Wnet / QA x 100 %
= mR(T1 – T4) ln P1 / P2 x 100 %
mRT1 ln P1 / P2
= T1 – T4 x 100 %
T1
ecc = TH – TL x 100 %
TH
6. Carnot Cycle Mean Effective Pressure, Pm
Pm = Wnet / VD
= Wnet / (V3 – V1)
Pm = ecc x QA / (V3 – V1)
SEATWORK:
1. A Carnot Cycle engines uses 0.5 kg/s of air as the working substance. The pressure and temperature at the
start of isothermal expansion are 1 MPa and 370 °C respectively. If the isothermal expansion ratio is 4 and
the adiabatic expansion ratio is 2, determine:
a. The heat added ans. 127.91 kJ/s
b. The heat rejected ans. -96.94 kJ/kg
c. The thermal efficiency ans. 24.21 %
d. The mean effective pressure ans. 47.94 kPa
2. An air-standard Carnot Cycle is executed in a closed system between the temperature limits of 350 and 1200
K. The pressures before and after the isothermal compression are 150 kPa and 300 kPa, respectively. If the
network output per cycle is 400 kJ, determine:
a. The maximum pressure in the cycle ans. 22388.11 kPa
b. The heat transfer in air, QA ans. 564.71 kJ
c. The mass of air ans. 2.37 kg
Note: Use Rair = 0.287 kJ/kg-K
k = 1.4
if not given in the problem
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